Research for Game Theory

A differential game is one in which, as the action progresses, both the environment and the decisions available to the players are subject to a consistent, logical law, so that the problem is amenable to mathematical analysis. Usually, the action is continuous, and solutions can actually be obtained for a wide range of problems of extended conflict between two antagonists. The applications include various models of battles, pursuit and evasion games, dogfights and other contests of maneuvering, such as football, and some aiming and evasion problems. By allowing one player to be passive, certain programs can be optimized. A chapter is devoted to collision avoidance, in which the players cooperate rather than conflict. In what are termed games of degree the players respectively seek to maximize and minimize some numerically valued payoff. In games of kind the criterion is sharp, such as whether or not capture will occur in a pursuit situation. The two types have separate but related theories. The text concludes with chapters on the case of incomplete information and the practical aspects of applications to warfare. This is not a revised version. It was assigned a .10 version because under an original numbering system which was abandoned, there were two CNA RC's numbered 1.